CBSE CLASS 10 · MATHS & SCIENCE

Class 10 Linear Equations MCQ Practice

Five questions to see what clicks. Then we’ll unpack your answers together and help you choose what to practise next.

01 Have a go02 Understand why03 Try a fresh question

MATHS / CLASS 105 QUESTIONS

2x + y = 7

LINEAR EQUATIONS

Crack the equation.

Turn clues into equations, solve the pair and see where the lines meet.

5 questions3 ideas to exploreHints if you need them

No sign-up · No negative marking · 10 seconds to think before each next question

Want a quick warm-up first?

Linear equations: model, solve and classify — TutorMax original questions

Model the conditions

Define each variable with units and translate each condition separately. Item count multiplies item price.

Eliminate and check

Add or subtract complete equations. Divide by the remaining coefficient, then substitute into both original conditions.

Classify shared solutions

A contradiction gives no solution. A repeated equation leaves infinitely many points. Coefficient proportionality alone is not enough: check the constants.

You can open a hint during the challenge too. We’ll show where a hint helped in your report.

Let’s practise with the notes insteadTurn on JavaScript for the question-by-question activity. You can still read these notes and have a go at the questions below.

Linear equations: model, solve and classify — TutorMax original questions

Model the conditions: Define each variable with units and translate each condition separately. Item count multiplies item price.

Eliminate and check: Add or subtract complete equations. Divide by the remaining coefficient, then substitute into both original conditions.

Classify shared solutions: A contradiction gives no solution. A repeated equation leaves infinitely many points. Coefficient proportionality alone is not enough: check the constants.

Two notebooks and a pen cost ₹70; one notebook and a pen cost ₹40. If n is notebook price and p is pen price, which pair models this?

2n+p=70; n+p=40
n+2p=70; n+p=40
2n+p=40; n+p=70

Let’s work through the answer

Define n and p in rupees. Translate each purchase separately: 2n+p=70 and n+p=40.

Solve 3a+b=29 and a+b=15. What are a and b?

a=7, b=8
a=14, b=1
a=8, b=7

Let’s work through the answer

Subtract the second equation from the first: 2a=14, so a=7. Then b=15−7=8. Check 3×7+8=29.

For x+y=11 and x−y=3, which pair is a solution?

x=7, y=4
x=4, y=7
x=14, y=3

Let’s work through the answer

Add to obtain 2x=14, so x=7. Substitute y=4 and check 7−4=3.

How many solutions do x+y=4 and 2x+2y=10 have?

None
One
Infinitely many

Let’s work through the answer

Doubling x+y=4 gives 2x+2y=8. The second equation contradicts it; the lines are distinct and parallel.

How many solutions do 2x+3y=12 and 4x+6y=24 have?

Infinitely many
None
Exactly two

Let’s work through the answer

Every term in the first equation doubles to the second. The same line is written twice.

Keep practising Maths for free →

About this preview & your answers

These are original TutorMax practice questions, not official board-paper questions. We’re still checking their fit with the 2026–27 syllabus. Five questions give us a starting point, not a predicted board grade or a complete picture of a chapter.

No login is needed. Your answers stay in this tab while you practise. Resetting or reloading clears them; this tool doesn’t save or send them.